PROBLEM 2 A trough is to be constructed as in the figure shown below (note dimensions are in feet). The only variable in

[answerhappygod]

Problem 2 A Trough Is To Be Constructed As In The Figure Shown Below Note Dimensions Are In Feet The Only Variable In 1 (154.1 KiB) Viewed 25 times

PROBLEM 2 A trough is to be constructed as in the figure shown below (note dimensions are in feet). The only variable in the problem is the angle (which in turn causes the height and top width of the trapezoidal face to vary. We wish to find the value of that will maximize the volume of the trough, the dimensions of the front face (height and top base), and what that maximum volume is. The hardest part of this problem will be setting up the function to maximize, so be sure to walk through the hints that step you through that. This is in part testing that you can read math instructions. 20 Want: What is it you want to maximize? What is the formula for that thing? It helps to know that the volume of a solid of this type is just the face area multiplied by the length dimension. Volume of the trough will be the area of that trapezoid times 20, so really you just need to look up the formula for area of a trapezoid. The formula at the outset should have symbols that represent the top and bottom bases the height of trapezoid. Have: The short base of the trapezoid is fixed at 1, but you need to work into the expressions for the height and the top base. Use a little trigonometry... What is the expression for the height in terms of ? What is the expression for the top base in terms of ? Solve and stuff to create one function. Now you can get V as a function of O and continue on with the process. Take it from there (no more hints). Take the function through the optimization process. OK to ask Symbolab to check your equation, but for full credit, you need to show the solution process (the equation that leads to the critical values is a quadratic in sine and is hand-solvable). Be sure you show some sort of test the verifies you are getting a value that leads to a maximum. Answer clearly at the end everything the question asks for, using sentences and units. Round final answer for volume to one decimal place. Answer the question with values rounded to two places (angle can be exact) using correct units. Answer should use sentences. Be sure to include the values of the angle that maximizes the volume, the dimensions (height and top base) of the front of the trough, and the value of the maximum volume.